1) Mathematical terminology 
The principle of Irreducibility, in philosophy, has the sense that a complete account of an entity will not be possible at lower levels of explanation and which has novel properties beyond prediction and explanation. Another way to state this is that Occam`s razor requires the elimination of only those entities that are unnecessary, not as many e....[mathematics] In mathematics, the concept of irreducibility is used in several ways. The notions of irreducibility in algebra and manifold theory are related. An n-manifold is called prime, if it cannot be written as a connected sum of two n-manifolds (neither of which is an n-sphere). An irreducible manifold is thus prime, although the con...
• (n.) The state or quality of being irreducible.
Ir`re·du`ci·bil'i·ty noun The state or quality of being irreducible.